No, you shouldn’t swap the verb complement from continuous
form to its infinitive form as you’ve suggested doing.
The change in aspect would subtly alter the meaning:
they are not equivalent.
If you did that, it would mean something else subtly different.
Look at it this way:
If your mother had you eat your peas, then that means she made you eat the
peas, and they are are now eaten and done with.
In contrast, if she had you eating your peas, she did something to
leave you in the state that you were (still!) eating your peas, not that
you had already finished doing so as in the original.
When you use the verb have in a transitive way with an object and then
another complement, that complement expresses either (1) the action that the
subject causes the object to take, or (2) the resulting condition of the object
caused by that subject.
All this falls under OED sense #28 for the verb have: [paywalled link]
- transitive. With complement expressing an action or state caused by the subject.
Also with will or would indicating volition or requirement; cf. will v.¹ 40a.
Both your examples are of this sort. The difference between them is that
the first uses a bare infinitive for its complement, while the second uses
the progressive ‑ing form for its complement. Here are examples from
each of the OED’s four subsenses for sense 2, varying by the type of complement:
- He had the guns counted. (complement is past participle)
- She had them in tears. (other complement)
- What would you have me do? / I'll have you know. (complement is bare infinitive)
- He had them rolling in the aisles. (complement is ‑ing verb)
Both your examples are non-finite verb phrases/clauses, but they mean
slightly different things, corresponding to the third and fourth OED
subsenses for sense 28.
The third subsense is this one:
c. With bare infinitive (formerly also †to-infinitive, †at and infinitive) as complement.
(a) To induce, prevail upon, or compel (a person) or to succeed in causing
(a thing) to do something; e.g. what would you have me do? Also (in
weakened sense): to cause or set (a person) to do something for one. Cf.
get v. 28a.
Also occasionally with passive infinitive: to
cause or compel to undergo the specified action; cf. sense 28a.
also I'll have you know at Phrases 3b.
In simpler words, it means to “make” someone do the specified action. So
she had me eat peas could have been written she made me eat peas
instead. Those two mean the same thing.
The fourth subsense is the type being used in your three original
- d. With present participle as complement. To compel, induce, arrange for (a
person or thing) to be doing something; e.g. he had them rolling in the
aisles. Cf. get v. 31b.
So the difference here is one of aspect. The (c) case is a bare infintive
so there is no continuous aspect involved. The (d) case by using the ‑ing form
of the verb uses the continuous aspect to convey that the action was an ongoing one,
that it was in progress.
Here for the record are the first two subsenses from the OED:
a. With past participle as complement. To cause or arrange for the
specified action to be performed on (a person or thing); e.g. he had the
guns counted. Cf. get v. 29a(a).
b. With complement. To bring into the specified state or condition, esp.
deliberately; to cause to become; to make, render; e.g. she had them in
tears. Cf. get v. 26a(a).